Latifi Alavijeh Milad

Finite Volume Methods Applied to Water Hammer Problems with Complex Boundary Conditions

Abstract

Water hammer manifests itself as large pressure fluctuations in piping systems. Analyzing the water hammer is an important part of designing water pipelines. So far, many different methods have been proposed for analyzing this phenomenon. In this study, the finite volume method (FVM) is applied to solve water hammer problems with complex boundary conditions. The non-linear partial differential continuity and momentum equation are discretized and values of pressure head and velocity in each cell at new time step is computed using the values at the previous time step, flux differences at interfaces, and values of source term. The flux difference is calculated using the one-step Roe’s method. In addition, Method of Characteristics (MOC) with spatial interpolation is applied to compute the boundary values. Boundary conditions which are considered in this research include reservoirs, valves, series pipes, pumps (with constant speed and shut-off), surge tanks, and air chambers. The results are compared to other numerical methods predictions and experimental data. It is observed that Roe’s scheme results depend on the courant number (Cr), and courant number should be close to 1.0 to obtain accurate results. Furthermore, Roe’s scheme results were similar to MOC results and experimental data. It is concluded that at low courant numbers, a decrease in cell numbers leads to an increase in the numerical dissipation. It is shown that the first-order Roe’s scheme is identical to MOC scheme with space-line interpolations. However, for a given level of accuracy, the FVM normally requires more execution times.